Flat Earth Big Bowl

As the sun's glow fades and your eyes become accustomed to the night, the sky gradually fills with stars. Thousands of them shimmer blue, silvery white, some gold, some reddish, seemingly set into a great dark bowl, the celestial sphere, overarching the flat earth on which you stand.

Thousands of stars in the night sky?

Maybe that number has brought you back through a starlit ten thousand years and into the incandescent lamp light of your living room or kitchen or bedroom or wherever you are reading this: "I've never seen thousands of stars!" you protest.

We said earlier that, from many locations, our sky is spoiled. The sad fact is that, these days, fewer and fewer of us can see anything like the three thousand or so stars that should be visible to the naked eye on a clear evening. Ten thousand years ago, the night sky was not lit up with the light pollution of so many sources of artificial illumination. Unless you sail far out to sea or travel to the high, dry desert of the Southwest, you might go through your entire life without really seeing the night sky, at least not the way our ancestors saw it.

Man in the Moon

Even in our smog- and light-polluted skies, however, the Moon shines bright and clear. Unlike the Sun, which appears uniform, the surface of the Moon has details we can see, even without a telescope. Even now, some three decades after human beings walked, skipped, and jumped on the Moon and even hit a golf ball across the lunar surface, the Moon holds wonder. Bathed in its silver glow, we may feel a connection with our ancestors of 10 millennia ago. Like them, we see in the lunar blotches the face of the "Man in the Moon."

Neil Armstrong took this picture of fellow astronaut "Buzz" Aldrin about to join him on the surface of the Moon, July 20, 1969.

(Image from arttoday.com)

If the face of the Moon presented a puzzle to our ancestors, they were also fascinated by the way the Moon apparently changed shape. One night, the Moon might be invisible (a new moon); then, night by night, it would appear to grow (wax), becoming a crescent; and, by one week later, be a quarter moon (which is a half moon in shape). Through the following week, the Moon would continue to wax, entering its gibbous phase, in which more than half of the lunar disk was seen. Finally, two weeks after the new moon, all of the lunar disk would be visible: The full moon would rise majestically at sunset. Then, through the next two weeks, the Moon would appear to shrink (wane) night after night, passing back through the gibbous, quarter, and crescent phases, until it became again the all-but-invisible new moon.

Gibbous is a word from Middle English that means "bulging"—an apt description of the Moon's shape between its quarter phase and full phase.

Star Words

Gibbous is a word from Middle English that means "bulging"—an apt description of the Moon's shape between its quarter phase and full phase.

Close Encounter

Close Encounter

For untold generations, people have discerned a human face in the crater-scarred markings of the Moon. The Man in the Moon is sometimes interpreted as an old woman cooking. Among Native Americans, the face or faces in the Moon have been described (for example) as a frog charged with protecting the Moon from a bear who would otherwise swallow it. An ancient Scandinavian folktale speaks of Hjuki and Bill, perhaps the original Jack and Jill, who, carrying a pail of water, tumbled down a hill as they ran from their cruel father. They were rescued by the embrace of the Moon. For Scandinavian kids, the "Man in the Moon" is the image of Hjuki and Bill, complete with pail.

The cycle takes a little more than 29 days, a month, give or take, and it should be no surprise that the word "month" derived from the word "moon." In fact, just as our ancestors learned to tell the time of day from the position of the Sun, so they measured what we call weeks and months by the lunar phases. The lunar calendar is of particular importance in many world religions, including Judaism and Islam. For those who came before us, the sky was more than something to marvel at. It could also be used to guide and coordinate human activity. As we will see in Chapters 2 and 3, the ancients became remarkably adept at using the heavens as a great clock and calendar.

The phases of the Moon. The globe in the center is Earth. The inner circle shows how the sunlight illuminates the Moon as it orbits Earth. The outer circle shows how the Moon appears from Earth.

(Image from the authors' collection)

Lights and Wanderers

Ten thousand years ago, family time at night was not occupied with primetime sitcoms followed by the news and David Letterman. Our ancestors were not glued to television screens, but presumably to the free show above, the celestial sphere. Early cultures noticed that the bowl above them rotated from east to west. They concluded that what they were seeing was the celestial sphere—which contained the stars—rotating, and not the individual stars. All the stars, they noticed, moved together, their positions relative to one another remaining unchanged. (That the stars "move" because of Earth's rotation was a concept that lay far in the future.)

The coordinated movement of the stars was in dramatic contrast to something else the ancient sky watchers noticed. While the vast majority of stars were clearly fixed in the rotating celestial sphere, a few—the ancients counted five—seemed to meander independently, yet regularly, across the celestial sphere. The Greeks called these five objects planetes, "wanderers," and, like nonconformists in an otherwise orderly society, the wanderers would eventually cause trouble. Their existence would bring the entire heavenly status quo into question and, ultimately, the whole celestial sphere would come crashing down.

Celestial Coordinates

But we're getting ahead of our story. In Chapter 4, "Astronomy Reborn: 1543-1687," you'll find out why we no longer believe that the celestial sphere represents reality; however, the notion of such a fixed structure holding the stars is still a useful model for us moderns. It helps us to communicate with others about the positions of the objects in the sky. We can orient our gaze into the heavens by thinking of the point of sky directly above the earth's North Pole as the north celestial pole, and the point below the South Pole as the south celestial pole. Just as the earth's equator lies midway between the North and South Poles, so the celestial

Star Words

Declination is the angular distance (distance expressed as an angle rather than in absolute units, such as feet or miles) north or south of the celestial equator. It is akin to lines of latitude on the earth.

Star Words

Declination is the angular distance (distance expressed as an angle rather than in absolute units, such as feet or miles) north or south of the celestial equator. It is akin to lines of latitude on the earth.

Astronomer's Notebook

Declination is analogous to Earthly latitude. The declination of a star seen directly above the earth's equator would also be at the celestial equator—that is, 0 degrees. A star at the north celestial pole (that is, directly over the earth's North Pole) would be +90 degrees. At the south celestial pole, it would be -90 degrees. In the latitudes of the United States, stars directly overhead have declinations in the +30- to +40-degree ranges. The Bradley Observatory at Agnes Scott College is at a latitude of 33 deg, 45 min, 55.84 sec. That means that in Decatur, GA, the North Star (Polaris) is about 34 degrees above the northern horizon.

equator lies equidistant between the north and south celestial poles. Think of it this way: If you were standing at the North Pole, then the north celestial pole would be directly overhead. If you were standing at the equator, the north and south celestial poles would be on opposite horizons. And if you were standing at the South Pole, the south celestial pole would be directly overhead.

Astronomers have extended to the celestial sphere the same system of latitude and longitude that describes earthly coordinates. The lines of latitude, you may recall from geography, run parallel with the equator and measure angular distance north or south of the equator. On the celestial sphere, declination (dec) corresponds to latitude and measures the angular distance above or below the celestial equator. While earth-bound latitude is expressed in degrees north or south of the equator (Philadelphia, for instance, is 40 degrees north), celestial declination is expressed in degrees + (above) or - (below) the celestial equator. The star Betelgeuse, for example, is at a declination of +7 degrees, 24 minutes.

On a globe, the lines of longitude run vertically from pole to pole. They demarcate angular distance measured east and west of the so-called prime meridian (that is, 0 degrees), which by convention and history has been fixed at Greenwich Observatory, in Greenwich, England. On the celestial sphere, ^ o right ascension (R.A.) corresponds to longitude. While declination is measured in degrees, right ascension is measured in hours, minutes, and seconds, increasing from west to east, starting at 0. This zero point is taken to be the position of the sun in the sky at the moment of the vernal equinox (we'll discuss this in Chapter 3, "The Unexplained Motions of the Heavens''). Because the earth rotates once approximately every 24 hours, the same objects will return to their positions in the sky approximately 24 hours later. After 24 hours, the earth has rotated through 360 degrees, so that each hour of R.A. corresponds to 15 degrees on the sky.

If the celestial poles, the celestial equator, and declination are projections of earthly coordinates (the poles, the equator, and latitude), why not simply imagine R.A. as projections of lines of longitude?

There are good reasons why we don't. Think of it this way: The stars in the sky above your head in winter time are different than those in summer time. That is, in the winter we see the constellation Orion, for example, but in summer, Orion is gone, hidden in the glare of a much closer star, the sun. Well, although the stars above you are changing daily, your longitude (in Atlanta, for example) is not changing. So the coordinates of the stars cannot be fixed to the coordinates on the surface of the earth. As we'll see in later chapters, this difference comes from the fact that in addition to spinning on its axis, the earth is also orbiting the sun.

Star Words

Right ascension is a coordinate for measuring the east-west position of objects in the sky.

Star Words

Right ascension is a coordinate for measuring the east-west position of objects in the sky.

Measuring the Sky

The true value of the celestial coordinate system is that it gives the absolute coordinates of an object, so that two observers, anywhere on Earth, can direct their gaze to the exact same star. When you want to meet a friend in the big city, you don't tell her that you'll get together "somewhere downtown." You give precise coordinates: "Let's meet at the corner of State and Madison streets." Similarly, the right ascension and declination astronomers use tell them (and you) precisely where in the sky to look.

The celestial coordinate system can be confusing for the beginning sky watcher and is of little practical value to an observer armed with nothing but the naked eye. However, it can help the novice locate the North Star, and to know approximately where to look for planets.

There is a simpler way to measure the location of an object in the sky as observed from your location at a particular time. It involves two angles. You can use angles to divide up the horizon by thinking of yourself as standing at the center of a circle. A circle may be divided into 360 degrees (and a degree may be subdivided into 60 minutes, and a minute sliced into 60 seconds). Once you decide which direction is 0 degrees (the convention is to take due north as 0 degrees), you can measure, in degrees, precisely how far an object is from that point. Now that you have taken care of your horizontal direction, you can fix your vertical point of view by imagining an upright half circle extending from horizon to horizon. Divide this circle into 180 degrees, with the 90-degree point directly overhead. Astronomers call this overhead point the zenith.

Altitude and azimuth are the coordinates that, together, make up the altazimuth coordinate system, and, for most people, they are quite a bit easier to use than celestial coordinates. An object's altitude is its angular distance above the horizon, and its compass direction, called azimuth, is measured in degrees increasing clockwise from due north. Thus east is at 90 degrees, south at 180 degrees, and west at 270 degrees.

Altazimuth coordinates, while perhaps more intuitive than the celestial coordinate system, do have a serious shortcoming. They are valid only for your location on Earth at a particular time of day or night. In contrast, the celestial coordinate system is universal because its coordinate system moves with the stars in the sky.

The Size of Things, or "I Am Crushing Your Head!"

In a television show called Kids in the Hall, there was a character who would look at people far away through one eye and pretend to crush their heads between his thumb and forefinger. If you try this trick yourself, you'll notice that people have to be at

Star Words

Altazimuth coordinates are altitude (angular distance above the horizon) and azimuth (compass direction expressed in angular measure).

Star Words

Altazimuth coordinates are altitude (angular distance above the horizon) and azimuth (compass direction expressed in angular measure).

least five or so feet away for their heads to be small enough to crush. Their heads don't actually get smaller, of course, just the angular size of the head does. In fact, you can use this same trick (if sufficiently distant) to crush cars, or planes flying overhead. All because of the fact that as things get more distant, they appear smaller— their angular size is reduced.

The surface of the earth is real and solid. You can easily use absolute units such as feet and miles to measure the distance between objects. The celestial sphere, however, is an imaginary construct, and we do not know the distances between us and the objects. In fact, simply to locate objects in the sky, we don't need to know their distances from us. We get that information in other ways, which we will discuss in several chapters. Now, from our perspective on Earth, two stars may appear to be separated by the width of a finger held at arm's length when they are actually many trillions of miles distant from each other. You could try to fix the measurement between two stars with a ruler, but where would you hold the measuring stick? Put the ruler close to your eye, and two stars may be a quarter-inch apart. Put it at arm's length, and the distance between those same two stars may have grown to several inches.

Astronomers use angular size and angular separation to discuss the apparent size on the sky or apparent distance between two objects in the sky. For example, if two objects were on opposite horizons, they would be 180 degrees apart. If one were on the horizon and the other directly overhead, they would be 90 degrees apart. You get the picture. Well, a degree is made up of even smaller increments. One degree is made up of 60 minutes (or arcminutes), and a minute is divided into 60 seconds (arcseconds).

Let's establish a quick and dirty scale. The full moon has an angular size of half a degree, or 30 arcminutes, or 1,800 arcseconds (these are all equivalent). The "smallest" celestial object the human eye can resolve is about 1 arcminute across. The largest lunar craters are about 2 arcminutes across, and separating objects that are 1-2 arcseconds apart is impossible (at least at optical wavelengths) from all but the best sites on Earth. This difficulty is due to atmospheric turbulence and is a limitation of current ground-based optical observing. Now that you know the full moon is about half a degree across, you can use its diameter to gauge other angular sizes.

Angular size and angular separation are size and distance expressed as angles on the sky rather than as absolute units (such as feet or miles). Since many of these measurements are less than a full degree, we point out that a degree is made up of 60 arcminutes and an ar-cminute of 60 arcseconds.

Star Words

Angular size and angular separation are size and distance expressed as angles on the sky rather than as absolute units (such as feet or miles). Since many of these measurements are less than a full degree, we point out that a degree is made up of 60 arcminutes and an ar-cminute of 60 arcseconds.

To estimate angles greater than a half-degree, you can make use of your hand. Look at the sky. Hold your hand upright at arm's length, arm fully extended outward, the back of the hand facing you, your thumb and index finger fully and stiffly extended, your middle finger and ring finger folded in, and your pinky also fully extended. The distance from the tip of your thumb to the tip of your index finger is about 20 degrees (depending on the length of your fingers!). From the tip of your index finger to the tip of your pinky is 15 degrees; and the gap between the base of your index finger and the base of your pinky is about 10 degrees.

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